The relation R defined on the set of natural | vedclass

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(A) The relation $R$ is defined on the set of natural numbers $N$ as $\{(a, b) : |a - b| = 3\}$.
This implies $a - b = 3$ or $b - a = 3$.
If $a - b

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$\{(1, 4), (2, 5), (3, 6), \dots\}$

Vedclass · Answer

(A) The relation $R$ is defined on the set of natural numbers $N$ as $\{(a, b) : |a - b| = 3\}$.
This implies $a - b = 3$ or $b - a = 3$.
If $a - b = 3$,then $a = b + 3$. For $b = 1, 2, 3, \dots$,the pairs are $(4, 1), (5, 2), (6, 3), \dots$.
If $b - a = 3$,then $b = a + 3$. For $a = 1, 2, 3, \dots$,the pairs are $(1, 4), (2, 5), (3, 6), \dots$.
The complete relation is $\{(a, b) : |a - b| = 3\} = \{(1, 4), (4, 1), (2, 5), (5, 2), (3, 6), (6, 3), \dots\}$.

The relation $R$ defined on the set of natural numbers as $\{(a, b) : a\}$ differs from $b$ by $3\}$ is given by

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